How do I test if it is a mersenne prime on GIMPS?

[spkarra]

Originally Posted by Batalov

This one is fine to test, but you still have steps 2, 3 and 4 to do.
Step 2. Small factors are not tested deep enough. (wanted level is 2^74. Makes sense to do all factoring de novo.)
Step 3. P-1 test has not been run
Step 4. L-L test has not been run

Why are they done in this order? (and why do you not want to skip steps?)
Because each step takes more time than the previous.

You can reserve this number by starting running it in your own copy of Prime95 that is configured to communicate to the GIMPS server. Your program will communicate and will have it reserved. then you can pause your Prime95 (or you can run it on and off) but start factoring in mfaktc in parallel. If you don't have a graphics card, take some other exponent that already has steps 2 and 3 done. Read the instructions at http://www.mersenne.org/gettingstarted/ and optionally here on the forum (use the search function).

Thanks a lot Batalov.

I completed P-1 testing and got the results.txt. I updated in the GMIPS site, but unable to see in the list.

Anyhow, this is what I got in the results.txt:

[Fri Nov 14 17:38:38 2014]
UID: jrk1964/spxxxxxx, M93887011 completed P-1, B1=1680000, We4: 7D376A2C, AID: 154AB9E38AABE0DFCF9B2B35F214A23C


No idea what it meant by.

[Batalov]

It means that Step 3 did not "kill" your candidate. You now should trial factor some more, and then proceed to step 4 (most likely your computer is already running Step 4).

What do you see if you open a little icon with "2^P-1" on it?

[spkarra]

Originally Posted by TheMawn

You can manually reserve this exponent if you wish. First, however, you want to trial factor it. Probably to 74 - 76 bits. That will take some time, but not nearly as much as running the LL test in its entirety. A modern computer could take several weeks. A not-so-modern computer maybe a few months.

Yeah, I started running LL test on the prime that I reserved...close to 40% completion and keeping fingers crossed..

---------------------------------------------------
Nov 15 18:07 Restarting worker to do LL test.

Nov 15 18:07 Starting primality test of M93887011 AT ITERATION 222

Dec 1 16:10 Iteration: 17150000/93887011 [18.26%], ms/iter: 81.883 ETA: 72d 17:24


Dec 18 10:35 Iteration: 35220000/93887011 [37.51%] ms/iter: 78.956, ETA: 53D 14:41
-------------------------------------------------

Thanks,
Sastry Karra

[ewmayer]

Originally Posted by TheMawn

I have always wondered if the residue at the end of a test could give any insight into the number itself. Does it hold any value or is it random gibberish?

Only if the residue was worth anything would there be any reason at all to run the primality test on a known composite.

As with the Pe'pin test residue for Fermats, the LL test residue for Mersennes can be used to effect a very fast cofactor-probable-primality test, assuming at least one prime factor is known, or found at some later date.

[TheMawn]

Originally Posted by ewmayer

As with the Pe'pin test residue for Fermats, the LL test residue for Mersennes can be used to effect a very fast cofactor-probable-primality test, assuming at least one prime factor is known, or found at some later date.

That's actually kind of neat.

I looked that up a bit and found some archived discussions on ndatech.com. It's Peter Montgommery, no less, who talks about that, but he's referring to a Fermat Base-3 residue.

From: Peter-Lawrence.Montgomery@...
Date: Wed, 27 May 1998 07:09:33 +0200 (MET DST)
Subject: Mersenne: Suyama test and LL (was: Fermat base-3 for LL?)

On 20 May 1998, Ernst Mayer wrote

> Dear All: time to clear up this Fermat-base-3 business once and
> for all (i.e. until the next wave of newbies start nattering about
> it without bothering to look through this list's archives first.)

(lines deleted)

> Now, you may be asking why I bothered to write such a program if the
> test is no faster than LL and moreover not definitive (at least regarding
> primality - it WILL tell you for sure if the number is composite.) The
> answer lies in the above program name. The base-3 test will not prove
> primality of an M(p), but it can be used to quickly test the status of
> any cofactor of an M(p) with one or more known factors. This is because
> the Fermat-base-3 residue of an M(p) can be used (as with the Pe'pin
> test, which is really just a Fermat-base-3 test of a Fermat number)
> to perform a so-called Suyama posttest of the cofactor of the number
> in question. The Suyama test is described in many references on NT,
> (e.g. Riesel's book) so I'll not repeat the full description here.
>
> That is, the ONLY advantage of the Fermat-base-3 test is that it
> yields a residue which, if the number proves composite, is still of
> further use, unlike the LL residue, which is useful only for results
> verification.

[Batalov]

Originally Posted by spkarra

...Dec 18 10:35 Iteration: 35220000/93887011 [37.51%] ms/iter: 78.956, ETA: 53d 14:41
-------------------------------------------------

Thanks,
Sastry Karra

You are lucky that this number doesn't have small factors (which you didn't check: TF from 70 to 74-75 bits was not done; it is now done).

[Batalov]

Originally Posted by TheMawn

That's actually kind of neat.

I looked that up a bit and found some archived discussions on ndatech.com. It's Peter Montgommery, no less, who talks about that, but he's referring to a Fermat Base-3 residue.

[/B]

PM later outlined how (full-length) LL residues can be used, though.

[ewmayer]

Originally Posted by Batalov

PM later outlined how (full-length) LL residues can be used, though.

Yes - keep following that 'thread' in the next 1 or 2 M-digests and you should come across the generalization Serge mentions.

[spkarra]

Thanks Batalov. I will surely keep in mind to test upto 74-bits before starting LL in future.

[spkarra]

Originally Posted by spkarra

Thanks Batalov. I will surely keep in mind to test upto 74-bits before starting LL in future.

Almost 76.19% completed, ETA 20 more days.....

[R.D. Silverman]

Originally Posted by spkarra

Almost 76.19% completed, ETA 20 more days.....

Off topic. I see no discussion of mathematics here.